Calculating Maximum Compression in a Spring

[zaraox]

A 1.2 kilogram block is dropped from 0.48m above a spring in equilibrium. The force constant for the spring is 124 N/m. Calculate the maximum compression in the spring.

m = 1.2 kg
h = 0.48 + x
k = 124 N/m
x = ?

Ep = mgh
Ep = (1.2)(9.8)(0.48 + x)
Ep = 11.76(0.48 + x)
Ep = 5.6448 +11.76x


Sadly, that's as far as I get... if anyone could guide me through the next steps, it'd be greatly appreciated!

 

[mmattson07]

Energy is conserved when the block compresses the spring. So you can set up an equation to solve for the max distance d the spring will compress.

 

[zaraox]

Energy is conserved when the block compresses the spring. So you can set up an equation to solve for the max distance d the spring will compress.

I don't really follow. What equation do you suggest I use?

 

[mmattson07]

You know the initial K and U and u know at the max compression of the spring the energy is just the elastic potential energy 1/2kx^2 and you can set them equal because the energy is conserved

 

[zaraox]

Alright so:

5.6448 + 11.76x = (0.5)(124)(x^2)
5.6448 + 11.76x = 62x^2
62x^2 - 11.76x - 5.6448 = 0

Then I use quadratic formula and x comes out to be: x = 0.411 m

Is that right? :)

 

[mmattson07]

Looks good.